TY - JOUR
AU - Papangelou, F.
AB - Z. Wahrscheinlichkeitstheorie verw. Geb. 28,207-226 (1974) 9 by Springer-Verlag 1974 The Conditional Intensity of General Point Processes and an Application to Line Processes F. Papangelou* 1. Introduction An open problem in the theory of line processes is whether all stationary line processes in the plane with finite intensity and with a.s. no parallel lines are doubly stochastic Poisson processes ([1, 7]). In [7] it is proved that this is in fact the case for line processes whose Palm probability is absolutely continuous with respect to the unconditional probability, in a sense made precise there. A similar condition of absolute continuity for point processes on the real line led naturally to the "conditional random intensity measure" of the process, which as it turned out is essentially the natural increasing process in the Meyer decomposition of the given point process ([8, 9]). In the present paper we construct conditional intensity measures for point processes in abstract spaces and then show that roughly, every stationary line process in the plane whose conditional intensity measure is "sufficiently atomless" is a doubly stochastic Poisson process. This condition is not only sufficient, it is also necessary. However, the problem mentioned at the beginning remains unsolved, 
TI - The conditional intensity of general point processes and an application to line processes
JF - Probability Theory and Related Fields
DO - 10.1007/bf00533242
DA - 1974-09-01
UR - https://www.deepdyve.com/lp/springer-journals/the-conditional-intensity-of-general-point-processes-and-an-6cjoVzU5Wq
SP - 207
EP - 226
VL - 28
IS - 3
DP - DeepDyve
ER -